The circuit below was at position a for a long time. It is suddenly switched to

Question

The circuit below was at position a for a long time. It is suddenly switched to position b at time t=0.

A)  if the battery provides a voltage V = 2.00 V, the capacitor has C = 18.0 ?F and the resistor has R = 500.0 ?, what is the capacitor voltage Vc at time t = 1.0 ms?

B) In the previous problem, what is the total energy dissipated in the resistor after time t = 0?

C) For the circuit in the previous problem, consider the case when the switch is in position b for a long time, then switched to position a at time t = 0. What is the capacitor voltage Vc at time t = 2.0 ms?

Explanation / Answer

A)Given, R = 1000 Ohm ; C = 18 x 10-6 F ; Vb = 2 V ; t = 1 ms = 1 x 10-3 s

We know that, Vc = Vb e-t/RC

Vc = 2 x e-1 x 10-3/1000 x 18 x 10-6 = 2 x 0.946 = 1.89 Volts(aprox)

Hence, Vc = 1.89 Volts

B)Energy dissipated would be equal to U = 1/2 C V2

U = 0.5 x 18 x 10-6 x 1.89 x 1.89 = 3.2 x 10-5 J

Hence, U = 3.2 x 10-5 J

C)Vc = 2 - 1.89 = 0.11 V

Hence, Vc' = 0.11 Volts.

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